Oh, actually, just looking at the Surinder Singh rules, it’s marriage or nothing.
Only direct family members are eligible for Surinder Singh (I.e. spouse, child, parent). Unmarried Partners are considered extended family members and are not eligible for Surinder Singh.
Yes, they stopped unmarried partners using Singh to the UK as part of the Singh changes, after the ECJ said the non-EEA citizen abuse on their Singh Ruling to avoid the immigration rules of that EEA country, should be stopped. Just one of the many changes, all cleary mentioned in the UK's EEA Regulations and mentioned under the UK announcing changes to sections of the EEA Regs.
Partners are only Extended Family Members and have no automatic rights under EU laws. In 2017 the UK also brought in more changes that now stops some non-EEA citizens coming to the UK as Extended Family Members on Free Movement.
However the UK will now allow others to use Singh. e.g. their Brits can now be a Self Sufficient Qualified Person in another EEA country.
To use Singh, the non-EEA citizen needs to live in that EEA country with their Brit who is exercising treaty rights in a country that they are not a citizen of. The Brit must also now prove that their "centre of life" was in that EEA country to stop the Singh abuse.
The 17 year old girlfriend would need to be exercising her EU treaty rights in an EEA country they are not be a citizen of that country and it sounds like it's only her British citizen parents who are exercising treat rights? If that is the case, then that would make the OP an Extended Family Member and they are not allowed to use Singh to the UK anymore.
Even if the 17 year old was exercising treaty rights in a country she is not a citizen of, it will be difficult to prove Centre of Life for a spouse just joining her when she wants to live in the UK (go to university).
If everything can be met, it will take many months to get and RC in the Republic, and they have to be in the Republic for many months to pass the Centre of Life requirement.. Brexit and no trade deal means UK rules end in the UK on 29 March, no time to use the Singh Route to the UK.
Even if the OP reached the UK under the Singh Ruling, they are still the changes to the EEA Regs that the UK have brought in for those wanting to use Singh. e.g. their British citizen must now be an EU "qualified person” in the UK continuously for the non-EEA citizen to have a lawful right to be in the UK and for some that means they must buy a Comprehensive Sickness Insurance. Non-EEA citizens can be deported.
Plus on a Brexit, even if there is a trade deal and a Withdrawal agreement, nothing has been negotiated by the EU under that for non-EEA citizens using Singh, nor for some other non-EEA citizens using various EU routes to be in an EEA country. The EU stated that these being allowed to stay will be up to the UK government/future UK governments. Although those married to a British citizen can always apply for a spouse visa under UK immigration rules. Those already in the UK using Singh and refused the EU's PR or RC, or who know they will be refused PR as they don't meet the EEA Regs in the UK, are already changing to a UK spouse visa to start their 5 years to settlement again.